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# Two-Proportion Z-Test Risks

APSTAT-FPNE14

In a survey done in a small town last year, $8$ out of $12$ randomly selected people said they approve of the job the mayor is doing.

The following year, $10$ different people are randomly surveyed, and of these, only $6$ people approve.

Why would it be inappropriate to perform a two-proportion Z-test to determine whether the mayor’s approval rating has changed?

A

It is illogical to perform inferential procedures when the population data is already known.

B

The data does not come from simple random samples.

C

The populations are most likely NOT at least 10 times each sample.

D

At least one of the following is true:

${N}_{1}$*(pooled P)

${N}_{2}$*(pooled P)

${N}_{1}$*($1$-pooled p)

${N}_{2}$*($1$-pooled p)

E

The combined sample sizes are only $22$, which is too small.